I think this depends on whose POV we’re in. If it’s Darin’s then I think this would be more engaging with his (brief) perspective of being on fire. If it’s Kate’s POV, then why is she referring to herself by her full name and why aren’t we feeling any sense of urgency from her? If it’s a third character’s POV we’re in, the reader really does need to know that right away, before they form an attachment to either of the two characters mentioned here.

The first is hooky, the second is not, in my opinion. Ditto the comments on using a surname.

'One of the buckets of water that sat just outside' slows down the second sentence and puts the brakes on the urgency of the moment. Plus, the fact that there are several buckets of water on hand, means the incident is over before it begins.